Public Monitoring with Uncertainty in the Time Repetitions

This paper study repeated games where the time repetitions of the stage game are not known or controlled by the players. We call this feature random monitoring. Kawamori's (2004) shows that perfect random monitoring is always better than the canonical case. Surprisingly, when the monitoring is public, the result is less clear-cut and does not generalize in a straightforward way. Unless the public signals are sufficiently informative about player's actions and/or players are patient enough. In addition to a discount effect, that tends to consistently favor the provision of incentives, we found an information effect, associated with the time uncertainty on the distribution of public signals. Whether payoff improvements are or not possible, depends crucially on the direction and strength of these effects. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Public Monitoring, Moral Hazard, Stochastic Processes.

Regional variation in sex ratios and sex allocation in androdioecious Mercurialis annua.

In androdioecious metapopulations, where males co-occur with hermaphrodites, the absence of males from certain populations or regions may be explained by locally high selfing rates, high hermaphrodite outcross siring success (e.g. due to high pollen production by hermaphrodites), or to stochastic processes (e.g. the failure of males to invade populations or regions following colonization or range expansion by hermaphrodites). In the Iberian Peninsula and Morocco, the presence of males with hermaphrodites in the wind-pollinated androdioecious plant Mercurialis annua (Euphorbiaceae) varies both among populations within relatively small regions and among regions, with some regions lacking males from all populations. The species is known to have expanded its range into the Iberian Peninsula from a southern refugium. To account for variation in male presence in M. annua, we test the following hypotheses: (1) that males are absent in areas where plant densities are lower, because selfing rates should be correspondingly higher; (2) that males are absent in areas where hermaphrodites produce more pollen; and (3) that males are absent in areas where there is an elevated proportion of populations in which plant density and hermaphrodite pollen production disfavour their invasion. We found support for predictions two and three in Morocco (the putative Pleistocene refugium for M. annua) but no support for any hypothesis in Iberia (the expanded range). Our results are partially consistent with a hypothesis of sex-allocation equilibrium for populations in Morocco; in Iberia, the absence of males from large geographical regions is more consistent with a model of sex-ratio evolution in a metapopulation with recurrent population turnover. Our study points to the role of both frequency-dependent selection and contingencies imposed by colonization during range expansions and in metapopulations.

Indexes and boundaries for "quantitative significance" in statistical decisions.

Boundaries for delta, representing a "quantitatively significant" or "substantively impressive" distinction, have not been established, analogous to the boundary of alpha, usually set at 0.05, for the stochastic or probabilistic component of "statistical significance". To determine what boundaries are being used for the "quantitative" decisions, we reviewed pertinent articles in three general medical journals. For each contrast of two means, contrast of two rates, or correlation coefficient, we noted the investigators' decisions about stochastic significance, stated in P values or confidence intervals, and about quantitative significance, indicated by interpretive comments. The boundaries between impressive and unimpressive distinctions were best formed by a ratio of greater than or equal to 1.2 for the smaller to the larger mean in 546 comparisons, by a standardized increment of greater than or equal to 0.28 and odds ratio of greater than or equal to 2.2 in 392 comparisons of two rates; and by an r value of greater than or equal to 0.32 in 154 correlation coefficients. Additional boundaries were also identified for "substantially" and "highly" significant quantitative distinctions. Although the proposed boundaries should be kept flexible, indexes and boundaries for decisions about "quantitative significance" are particularly useful when a value of delta must be chosen for calculating sample size before the research is done, and when the "statistical significance" of completed research is appraised for its quantitative as well as stochastic components.

Steady-state expression of self-regulated genes.

MOTIVATION: Regulatory gene networks contain generic modules such as feedback loops that are essential for the regulation of many biological functions. The study of the stochastic mechanisms of gene regulation is instrumental for the understanding of how cells maintain their expression at levels commensurate with their biological role, as well as to engineer gene expression switches of appropriate behavior. The lack of precise knowledge on the steady-state distribution of gene expression requires the use of Gillespie algorithms and Monte-Carlo approximations. METHODOLOGY: In this study, we provide new exact formulas and efficient numerical algorithms for computing/modeling the steady-state of a class of self-regulated genes, and we use it to model/compute the stochastic expression of a gene of interest in an engineered network introduced in mammalian cells. The behavior of the genetic network is then analyzed experimentally in living cells. RESULTS: Stochastic models often reveal counter-intuitive experimental behaviors, and we find that this genetic architecture displays a unimodal behavior in mammalian cells, which was unexpected given its known bimodal response in unicellular organisms. We provide a molecular rationale for this behavior, and we implement it in the mathematical picture to explain the experimental results obtained from this network.

Medical image registration based on random line sampling

One of the key aspects in 3D-image registration is the computation of the joint intensity histogram. We propose a new approach to compute this histogram using uniformly distributed random lines to sample stochastically the overlapping volume between two 3D-images. The intensity values are captured from the lines at evenly spaced positions, taking an initial random offset different for each line. This method provides us with an accurate, robust and fast mutual information-based registration. The interpolation effects are drastically reduced, due to the stochastic nature of the line generation, and the alignment process is also accelerated. The results obtained show a better performance of the introduced method than the classic computation of the joint histogram

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

Mammalian genes are transcribed with widely different bursting kinetics.

In prokaryotes and eukaryotes, most genes appear to be transcribed during short periods called transcriptional bursts, interspersed by silent intervals. We describe how such bursts generate gene-specific temporal patterns of messenger RNA (mRNA) synthesis in mammalian cells. To monitor transcription at high temporal resolution, we established various gene trap cell lines and transgenic cell lines expressing a short-lived luciferase protein from an unstable mRNA, and recorded bioluminescence in real time in single cells. Mathematical modeling identified gene-specific on- and off-switching rates in transcriptional activity and mean numbers of mRNAs produced during the bursts. Transcriptional kinetics were markedly altered by cis-regulatory DNA elements. Our analysis demonstrated that bursting kinetics are highly gene-specific, reflecting refractory periods during which genes stay inactive for a certain time before switching on again.

The Limits of Discrete Time Repeated Games:Some Notes and Comments

This paper studies the limits of discrete time repeated games with public monitoring. We solve and characterize the Abreu, Milgrom and Pearce (1991) problem. We found that for the "bad" ("good") news model the lower (higher) magnitude events suggest cooperation, i.e., zero punishment probability, while the highrt (lower) magnitude events suggest defection, i.e., punishment with probability one. Public correlation is used to connect these two sets of signals and to make the enforceability to bind. The dynamic and limit behavior of the punishment probabilities for variations in ... (the discount rate) and ... (the time interval) are characterized, as well as the limit payo¤s for all these scenarios (We also introduce uncertainty in the time domain). The obtained ... limits are to the best of my knowledge, new. The obtained ... limits coincide with Fudenberg and Levine (2007) and Fudenberg and Olszewski (2011), with the exception that we clearly state the precise informational conditions that cause the limit to converge from above, to converge from below or to degenerate. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Pub- lic Monitoring, Moral Hazard, Stochastic Processes.

Role of Particle Shape on the Stress Propagation in Granular Packings

We present an experimental and numerical study on the influence that particle aspect ratio has on the mechanical and structural properties of granular packings. For grains with maximal symmetry (squares), the stress propagation in the packing localizes forming chainlike forces analogous to the ones observed for spherical grains. This scenario can be understood in terms of stochastic models of aggregation and random multiplicative processes. As the grains elongate, the stress propagation is strongly affected. The interparticle normal force distribution tends toward a Gaussian, and, correspondingly, the force chains spread leading to a more uniform stress distribution reminiscent of the hydrostatic profiles known for standard liquids

S-system parameter estimation for noisy metabolic profiles using newton-flow analysis.

Biochemical systems are commonly modelled by systems of ordinary differential equations (ODEs). A particular class of such models called S-systems have recently gained popularity in biochemical system modelling. The parameters of an S-system are usually estimated from time-course profiles. However, finding these estimates is a difficult computational problem. Moreover, although several methods have been recently proposed to solve this problem for ideal profiles, relatively little progress has been reported for noisy profiles. We describe a special feature of a Newton-flow optimisation problem associated with S-system parameter estimation. This enables us to significantly reduce the search space, and also lends itself to parameter estimation for noisy data. We illustrate the applicability of our method by applying it to noisy time-course data synthetically produced from previously published 4- and 30-dimensional S-systems. In addition, we propose an extension of our method that allows the detection of network topologies for small S-systems. We introduce a new method for estimating S-system parameters from time-course profiles. We show that the performance of this method compares favorably with competing methods for ideal profiles, and that it also allows the determination of parameters for noisy profiles.

Parameter estimation for the distribution of single cell lag times.

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level. We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.

Weak approximations. A Malliavin calculus approach

We introduce a variation of the proof for weak approximations that issuitable for studying the densities of stochastic processes which areevaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore if the inverse of the Malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations fordensities and distributions can also be achieved. We apply theseideas to the case of stochastic differential equations with boundaryconditions and the composition of two diffusions.

International business cycles, financial markets and household production

This paper investigates the properties of an international real business cycle model with household production. We show that a model with disturbances to both market and household technologies reproduces the main regularities of the data and improves existing models in matching international consumption, investment and output correlations without irrealistic assumptions on the structure of international financial markets. Sensitivity analysis shows the robustness of the results to alternative specifications of the stochastic processes for the disturbances and to variations of unmeasured parameters within a reasonable range.

Viability and Management of an Endangered Capercaillie (Tetrao urogallus) Metapopulation in the Jura Mountains, Western Switzerland

The populations of Capercaillie (Tetrao urogallus), the largest European grouse, have seriously declined during the last century over most of their distribution in western and central Europe. In the Jura mountains, the relict population is now isolated and critically endangered (about 500 breeding adults). We developed a simulation software (TetrasPool) that accounts for age and spatial structure as well as stochastic processes, to perform a viability analysis and explore management scenarios for this population, capitalizing on a 24 years-long series of field data. Simulations predict a marked decline and a significant extinction risk over the next century, largely due to environmental and demographic stochasticity (average values of life-history parameters would otherwise allow stability). Variances among scenarios mainly stem from uncertainties about the shape and intensity of density dependence. Uncertainty analyses suggest to focus conservation efforts on enhancing, not only adult survival (as often advocated for long-lived species), but also recruitment. The juvenile stage matters when local populations undergo extinctions, because it ensures connectivity and recolonization. Besides limiting human perturbations, a silvicultural strategy aimed at opening forest structure should improve the quality and surface of available patches, independent of their size and localization. Such measures are to be taken urgently, if the population is to be saved.